A Swiss Half Fare Card will definitely be cheaper than regular tickets. A Swiss Travel Pass is more convenient as you don't have to buy tickets for each trip, and it also includes many museums. You should do the math to be sure which option is cheaper. The below pages offer all the details:

Is this a business or leisure trip? I noticed you only included cities in your itinerary, and no mountains. If this is your first trip to Switzerland as a tourist, I'd recommend to visit at least one or two mountains. Note that there is not much to see in Interlaken. The surrounding area, including the Jungfrau region, is wonderful though.

Please see the mountain link I gave you for recommended day trips. All of them are wonderful, but some are summer trips only. Jungfraujoch and Schilthorn are options, as well as Mount Rigi (free with Swiss Travel Pass) and Pilatus (free with Swiss Travel Pass as of January 1, 2017).

Yes, all trips are fully covered. Please see the Swiss Travel Pass page I linked to, and click to the "Where it's valid" tab.